diff --git a/micall/core/contig_stitcher.py b/micall/core/contig_stitcher.py
index 1f05daa72..76d95afea 100644
--- a/micall/core/contig_stitcher.py
+++ b/micall/core/contig_stitcher.py
@@ -240,30 +240,52 @@ def stitch_2_contigs(left, right):
     return FrankensteinContig([left_remainder, overlap_contig, right_remainder])
 
 
-def stitch_contigs(contigs: Iterable[GenotypedContig]):
-    aligned = list(map(align_to_reference, contigs))
-
-    # Contigs that did not align do not need any more processing
-    yield from (x for x in aligned if not isinstance(x, AlignedContig))
-    aligned = [x for x in aligned if isinstance(x, AlignedContig)]
-
+def combine_overlaps(contigs: List[AlignedContig]) -> Iterable[AlignedContig]:
     # Going left-to-right through aligned contigs.
-    aligned = list(sorted(aligned, key=lambda x: x.alignment.r_st))
-    while aligned:
-        current = aligned.pop(0)
-
-        # Filter out all contigs that are contained within the current one.
-        # TODO: actually filter out if covered by multiple contigs
-        # TODO: split contigs that have big gaps in them first, otherwise they will cover too much.
-        aligned = [x for x in aligned if not current.contains(x)]
+    contigs = list(sorted(contigs, key=lambda x: x.alignment.r_st))
+    while contigs:
+        current = contigs.pop(0)
 
         # Find overlap. If there isn't one - we are done with the current contig.
-        overlapping_contig = find_overlapping_contig(current, aligned)
+        overlapping_contig = find_overlapping_contig(current, contigs)
         if not overlapping_contig:
             yield current
             continue
 
         # Replace two contigs by their stitched version, then loop with it.
         new_contig = stitch_2_contigs(current, overlapping_contig)
-        aligned.remove(overlapping_contig)
-        aligned.insert(0, new_contig)
+        contigs.remove(overlapping_contig)
+        contigs.insert(0, new_contig)
+
+
+def drop_completely_covered(contigs: List[AlignedContig]) -> List[AlignedContig]:
+    """ Filter out all contigs that are contained within other contigs. """
+
+    # TODO: filter out if covered by multiple contigs
+    # TODO: split contigs that have big gaps in them first, otherwise they will cover too much.
+
+    def find_most_covered(contigs) -> Optional[AlignedContig]:
+        for current in contigs:
+            if any(x for x in contigs if x != current and x.contains(current)):
+                return current
+
+    while contigs:
+        most_covered = find_most_covered(contigs)
+        if most_covered:
+            contigs.remove(most_covered)
+        else:
+            break
+
+    return contigs
+
+
+def stitch_contigs(contigs: Iterable[GenotypedContig]):
+    maybe_aligned = list(map(align_to_reference, contigs))
+
+    # Contigs that did not align do not need any more processing
+    yield from (x for x in maybe_aligned if not isinstance(x, AlignedContig))
+    aligned = [x for x in maybe_aligned if isinstance(x, AlignedContig)]
+
+    aligned = drop_completely_covered(aligned)
+
+    yield from combine_overlaps(aligned)
diff --git a/micall/tests/test_contig_stitcher.py b/micall/tests/test_contig_stitcher.py
index a00a1cfb5..234a6e753 100644
--- a/micall/tests/test_contig_stitcher.py
+++ b/micall/tests/test_contig_stitcher.py
@@ -201,19 +201,18 @@ def test_stitching_of_identical_contigs():
     # Scenario: The function correctly handles and avoids duplication when identical contigs are stitched together.
 
     ref_seq = 'A' * 100
-    contig = \
-        GenotypedContig(name='a',
+    contigs = [
+        GenotypedContig(name=name,
                         seq='ACTGACTG' * 100,
                         ref_name='testref',
                         ref_seq='ACTGACTG' * 100,
                         matched_fraction=1.0,
                         )
-
-    contigs = [contig, contig, contig]
+        for name in ["a", "b", "c"]]
 
     result = list(stitch_contigs(contigs))
     assert len(result) == 1
-    assert result[0].query == contig
+    assert result[0].query == contigs[2]
 
 
 def test_stitching_of_zero_contigs():